Pseudo‐random Gaussian distribution through optimised LFSR permutations

Abstract

Efficient hardware solutions to generate Gaussian-distributed random numbers are required in many applications. Linear feedback shift registers (LFSRs) are a low-complexity implementation of an approximated uniform pseudo-random distribution: multiple LFSRs can be used in combination to approximate a Gaussian distribution with a low complexity cost. The technique proposed in this work exploits the same principle but relies on a single LFSR and ad-hoc permutations of its bits to obtain an accurate approximation of a Gaussian distribution with low maximum autocorrelation, leading to a very low complexity implementation of a Gaussian pseudo-random number generator.